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Forum index » Science and Technology » Math » Recreational
Euler One
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Jim Dars
science forum beginner


Joined: 03 Jul 2005
Posts: 41

PostPosted: Tue Jun 20, 2006 7:49 pm    Post subject: Euler One Reply with quote
Hi All,

I was just rereading William Dunham's "Euler - Master of Us All". Not as
good as his wonderful "Journey Through Genius", but still a VERY interesting
book.

He points out Euler's solution(s) to find the value of

Sum (1 to infinity on k) k^-i where i is an even integer (see Euler
Two)

and remarks that no one has yet found solutions for i being an odd integer
greater than one. (Except for the 1978 "find" that for i=3 the answer is
irrational.) Has any progress yet been made?

Best wishes, Jim
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Frederick Williams
science forum addict


Joined: 19 Nov 2005
Posts: 97

PostPosted: Wed Jun 21, 2006 3:05 pm    Post subject: Re: Euler One Reply with quote
Jim Dars wrote:
Quote:

Hi All,

I was just rereading William Dunham's "Euler - Master of Us All". Not as
good as his wonderful "Journey Through Genius", but still a VERY interesting
book.

He points out Euler's solution(s) to find the value of

Sum (1 to infinity on k) k^-i where i is an even integer (see Euler
Two)

and remarks that no one has yet found solutions for i being an odd integer
greater than one. (Except for the 1978 "find" that for i=3 the answer is
irrational.) Has any progress yet been made?

Yes, see http://mathworld.wolfram.com/RiemannZetaFunction.html.

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